Small-disturbance stability optimization method for power systems based on random PV power output

Abstract

The present invention discloses a small-signal stability optimization method for a power system based on random PV output, which is applied to a power system with PV access and includes the following steps: 1. Quantify the uncertainty of PV output using an improved Bayesian neural network PV output prediction model modified based on a weighted Markov chain; 2. Use the eigenvalue method to perform small-signal stability analysis on the PV grid-connected power system under the scenario of PV output uncertainty to obtain system eigenvalues; 3. Optimize the parameters affecting the stable operation of the PV system based on the eigenvalue sensitivity model and system eigenvalues. Due to the randomness of environmental factors, PV output has strong randomness. The present invention takes the randomness of PV output into account during small-signal stability analysis, which is beneficial to improving the operation reliability of the power system with PV access.

Description

Technical Field

[0001] The present invention relates to the fields of photovoltaic output prediction and small-signal eigenvalue sensitivity calculation, and particularly to a small-disturbance stability optimization method for a photovoltaic grid-connected power system based on photovoltaic random variation. Background Art

[0002] The development of new energy power generation technology is rapid. The penetration rate of photovoltaic in the power system has increased year by year due to its unique advantages, which also makes its impact on the stable operation of the power system greater and greater. Therefore, it is extremely important to conduct small-disturbance stability analysis on the power system with photovoltaic access for the safe and stable operation of the power system.

[0003] Compared with traditional power generation systems, photovoltaic distributed power sources are deeply affected by external environmental factors such as solar irradiance and external temperature. These meteorological factors are highly random, so the photovoltaic output is random. However, when conducting small-signal stability analysis on the power system at present, it is carried out under the condition of determined output. Obviously, it is not effective to use the conventional small-signal stability analysis method to solve the stability problem of the photovoltaic grid-connected power system. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the above technologies and propose a small-disturbance stability optimization method for a power system based on photovoltaic random output, in order to be able to conduct small-signal stability analysis on the power system with photovoltaic access, thereby being beneficial to improving the operation reliability of the photovoltaic grid-connected power system.

[0005] The present invention adopts the following technical solutions to solve the technical problems:

[0006] A small-disturbance stability optimization method for a power system based on photovoltaic random output of the present invention is applied to a power system with photovoltaic access, and is characterized in that: the small-signal stability analysis method is carried out according to the following steps:

[0007] Step S1: Quantification of photovoltaic output uncertainty:

[0008] Step S1.1: Obtain weather characteristics, historical operation data of the photovoltaic power station and time factors and input them into the improved Bayesian neural network for prediction, obtain the predicted values of the photovoltaic output at each time point, and compare them with the corresponding actual values to obtain the relative error at each time point;

[0009] Step S1.2: Take the upper and lower limits where the relative error at any moment point is located as the state division value range, and obtain the state transition probability matrix of the relative error at the corresponding moment point for correcting the predicted value of the photovoltaic output at the corresponding time point, so as to obtain the corrected predicted values of the photovoltaic output at each time point;

[0010] Step S1.3: According to the state transition probability matrix, use the weighted Markov chain to correct the improved Bayesian neural network prediction model to obtain a corrected improved Bayesian neural network for outputting the predicted values of photovoltaic power generation at each future moment;

[0011] Step S2: Obtain the system eigenvalues corresponding to the predicted values of photovoltaic power generation at each future moment based on the eigenvalue method:

[0012] Step S2.1: Use the Lyapunov linearization method to process the equations describing the characteristics of the photovoltaic grid-connected power system to obtain the state equation matrix A of the photovoltaic grid-connected power system, and construct a mathematical relationship between the sensitivity of the system eigenvalue to the change in photovoltaic power generation and the sensitivity of the state equation matrix A to the change in photovoltaic power generation;

[0013] Step S2.2: Regard the randomness of photovoltaic power generation as a small disturbance in the photovoltaic grid-connected power system, obtain the sensitivity of the state equation matrix A to the change in photovoltaic power generation through the derivative method, and then obtain the sensitivity of the system eigenvalue to the change in photovoltaic power generation from the mathematical relationship;

[0014] Step S2.3: According to the predicted values of photovoltaic power generation at each future moment and the sensitivity of the system eigenvalue to the change in photovoltaic power generation, obtain the system eigenvalues corresponding to the predicted values of photovoltaic power generation at each future moment;

[0015] Step S3: Optimize the parameters affecting the stable operation of the photovoltaic system based on the sensitivity of the system eigenvalue to the operating parameters and control parameters of the photovoltaic grid-connected power system and the system eigenvalues corresponding to the predicted values of photovoltaic power generation at each future moment:

[0016] Step S3.1: Obtain the sensitivity of the system eigenvalue to the operating parameters and control parameters of the photovoltaic grid-connected power system to obtain the dominant variables affecting the system eigenvalue;

[0017] Step S3.2: Optimize the dominant variables of the system eigenvalue in the dangerous area. When all system eigenvalues are in the safe area, the optimization process ends to improve the stability of the photovoltaic grid-connected power system.

[0018] The feature of the small disturbance stability optimization method of the power system based on the random output of photovoltaic power generation described in the present invention also lies in that the step S2.3 includes:

[0019] S2.3.1: Let the sequence of predicted values of photovoltaic power generation at each future moment be denoted as P = {P pv1 , P pv2 , …, P pvj , …, P pvn}, and the corresponding time sequence to P is t = {t1, t2, …, t j , …, t n}, where t j represents the j-th moment, and P pvj represents the photovoltaic output prediction value at the j-th moment t j ;

[0020] S2.3.2: Let the initial moment be t0, then the photovoltaic output value at the initial moment t0 is denoted as P pv0 , and the i-th system eigenvalue at the initial moment t0 is denoted as Calculate the i-th system eigenvalue at the j-th moment t j using Equation (1)

[0021]

[0022] In Equation (1): k is the number of system eigenvalues; P PVj is the photovoltaic output prediction value at the j-th moment t j ; is the i-th system eigenvalue at the initial moment t0;

[0023] S2.3.3: Obtain the system eigenvalues λ corresponding to the photovoltaic output prediction values at future moments using Equation (2):

[0024]

[0025] The said step S3.1 includes:

[0026] Sa: Determine the photovoltaic system parameters to be optimized, including: operating parameters and control parameters; the operating parameter is the active power output P G of the synchronous generator SG; the control parameters are the k p parameters, k i parameters, including k p1 parameters, k i1 parameters, k p2 parameters, k i2 parameters, k p3 parameters, k i3 parameters, k p4 parameters, k i4 parameters;

[0027] Sb: Calculate the partial derivative of the variable affected by the operating parameter with respect to the operating parameter, and use it as an intermediate variable, so as to obtain the partial derivative of the state equation matrix A with respect to the operating parameter, which is the sensitivity of the system eigenvalue λ to the operating parameter;

[0028] Sb.1: Divide the state matrix A into four sub-matrices, denoted as A1, B1, C1, D1 respectively:

[0029] Sb.2: Obtain the variables in sub - matrix A1 affected by the active power output P of synchronous generator SG using Equation (3), including: variables composed of the operating parameters of synchronous generator SG G and variables composed of the operating parameters of photovoltaic operation

[0030]

[0031]

[0032] In Equation (3): X d is the direct - axis reactance of synchronous generator SG; T d ′0 is the direct - axis open - circuit transient time constant of synchronous generator SG; X d ′ is the direct - axis transient reactance of synchronous generator SG; N G and N P are the number of nodes of synchronous generator SG and photovoltaic nodes respectively; N G ×N G represents the dimension of sub - matrix A1 corresponding to the number of nodes of synchronous generator SG, and N P ×N P represents the dimension of sub - matrix A1 corresponding to the number of photovoltaic nodes; I d is the d - axis component of the current of synchronous generator SG; U dc is the DC capacitor voltage; C dc is the DC capacitance value; I gd , I gq are the d - axis and q - axis components of the grid - side current respectively; U gd , U gq are the d - axis and q - axis components of the grid - side voltage respectively

[0033] Sb3: Obtain the sensitivity of sub - matrix A1 to the active power output P G using Equation (4):

[0034]

[0035] In Equation (4): P Gm is the active power output of the m - th SG; (:, m) represents the m - th column of the matrix, and there is:

[0036]

[0037] Sb4: Obtain the variables in sub - matrix B1 affected by the active power output P of synchronous generator SG G using Equation (6), including: the first variable composed of the operating parameters of synchronous generator SG and the second variable

[0038]

[0039] Sb5: Obtain the sensitivity of the sub - matrix B1 to the active power output P using Equation (7): G

[0040]

[0041] And there is:

[0042]

[0043] Sb6: Obtain the variables in the sub - matrix C1 affected by the active power output P of the synchronous generator SG using Equation (9), including: the first variable composed of photovoltaic operation parameters G and the second variable

[0044]

[0045] Sb7: Obtain the sensitivity of the sub - matrix C1 to the active power output P using Equation (10): G

[0046]

[0047] Sb8: Obtain the variables in the sub - matrix D1 affected by the active power output P of the synchronous generator SG using Equation (11), including: the variables composed of the operation parameters of the synchronous generator SG G

[0048]

[0049] Sb9: Obtain the sensitivity of the sub - matrix D1 to the active power output P using Equation (12): G

[0050]

[0051] Sc: Obtain the sensitivity of the system eigenvalue λ to the active power output P using Equation (13): G

[0052]

[0053] In Equation (13): v is the right - multiplying matrix; w is the left - multiplying matrix; w T is the transpose of the left - multiplying matrix;

[0054] Sd: Obtain the sensitivity of the system eigenvalue λ to the control parameters:

[0055] Sd1: Obtain the sensitivity of the state matrix A to the k P1 parameter, k i1 ​​​​​​Partial derivative of parameters:

[0056]

[0057] In Equation (14): ω B is the reference value of the rotational speed of the synchronous generator SG;

[0058] Sd2: Calculate the partial derivative of the state matrix A with respect to the k P2 parameter, k i2 Partial derivative of parameters:

[0059]

[0060] Sd3: Calculate the partial derivative of the state matrix A with respect to the k P3 parameter, k i3 Partial derivative of parameters:

[0061]

[0062] Sd4: Calculate the partial derivative of the state matrix A with respect to the k P4 parameter, k i4 Partial derivative of parameters:

[0063]

[0064] Se: Obtain the sensitivity of the system eigenvalue λ with respect to the k Pa parameter, k ia parameters, where a = 1, 2, 3, 4:

[0065]

[0066] Sf: Select the variable corresponding to the maximum sensitivity as the dominant variable affecting the system eigenvalue.

[0067] An electronic device according to the present invention includes a memory and a processor, characterized in that the memory is used to store a program for supporting the processor to execute the small-signal stability optimization method, and the processor is configured to execute the program stored in the memory.

[0068] A computer-readable storage medium according to the present invention, characterized in that a computer program is stored on the computer-readable storage medium, and when the computer program is run by a processor, it executes the steps of the small-signal stability optimization method.

[0069] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0070] 1. Compared with the deterministic small-signal stability analysis of the power system, the present invention fully considers the randomness of photovoltaic output, and uses an improved Bayesian neural network modified by a weighted Markov chain to predict the photovoltaic output value at a future moment, thereby avoiding the poor optimization effect or even reverse optimization caused by the change of photovoltaic output.

[0071] 2. When predicting the photovoltaic output, the present invention uses a weighted Markov chain to correct the prediction result of the improved Bayesian neural network prediction model, making the predicted value of the photovoltaic output better fit the actual value, effectively improving the optimization effect of the subsequent operating parameters and control parameters of the photovoltaic system, and improving the operating reliability of the photovoltaic grid-connected system.

[0072] 3. The photovoltaic prediction model used in the present invention is the predicted value divided by time points, which improves the flexibility of parameter optimization and also improves the ability of the power system to cope with the change of photovoltaic output.

[0073] 4. The present invention has universality and is applicable not only to power systems with photovoltaic access, but also to wind power generation systems with the same output randomness and even power systems with both wind and light access. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a flowchart of the present invention;

[0075] Figure 2 is a flowchart of improving the photovoltaic output prediction accuracy of the improved Bayesian neural network using a weighted Markov chain;

[0076] Figure 3 is a flowchart of obtaining the system eigenvalues using the eigenvalue method;

[0077] Figure 4 is a distribution diagram of the eigenvalues of the safe area and the dangerous area. DETAILED DESCRIPTION OF THE INVENTION

[0078] The technical solution of the present invention will be specifically described below with reference to the drawings.

[0079] As Figure 1 shown, in this embodiment, a small-signal stability optimization method for a power system based on random changes of photovoltaic is carried out according to the following steps:

[0080] Step S1: Quantification of photovoltaic output uncertainty:

[0081] As Figure 2 shown, the quantification of photovoltaic output uncertainty is carried out according to the following steps:

[0082] S1.1: Obtain weather characteristics, historical operation data of the PV power station, and time factors, and input them into the improved Bayesian neural network for prediction to obtain the predicted values of PV power output at each time point, and compare them with the corresponding actual values to obtain the relative error at each time point;

[0083] S1.1.1: Consider input features such as time factors and weather factors. Use a fully connected neural network as the prediction model to predict the maximum PV output. Take the date of the prediction point, the single-day time, and the solar irradiance under the condition of no cloud cover as inputs, and the theoretical maximum output of the PV at this moment as the output. Divide the weather factors into sudden impact factors and persistent impact factors. To obtain information on persistent impact factors, use the t-SNE algorithm to perform preliminary feature extraction on the weather factors, and input the weather factors such as atmospheric pressure and temperature into the fully connected neural network after dimensionality reduction by t-SNE. The specific steps for the t-SNE algorithm to extract the data features of weather factors are as follows:

[0084] (1) Let C high-dimensional system operation data sets R = {x1, x2, …… x c}, and the conditional probability that these data points follow a Gaussian distribution pairwise is G j|i , as shown in Equation (1):

[0085]

[0086] In Equation (1): σ i is the variance of the Gaussian distribution of the data point x i .

[0087] (2) Calculate the joint probability distribution G ij of any two data points in the space from Equation (1), as shown in Equation (2):

[0088]

[0089] In Equation (2): d is the total number of data points.

[0090] (3) Let T = {α1, α2, ……, α e} be the mapping of the set R in the low-dimensional space that satisfies the t-distribution with degree of freedom l, and the joint probability distribution Q i of any two feature matrices of the system operation data can be obtained, as shown in Equation (3):

[0091] Q ij =(1 + ||α i - α j || 2 ) ∑ r≠l (1 + ||α r - α l || 2 )-1 (3)

[0092] In Equation (3): α is the mapping value of x with respect to the t-distribution.

[0093] (4) t-SNE uses the Kullback-Leibler divergence D KL to represent the accuracy of the mapping, as shown in Equation (4):

[0094]

[0095] (5) To maximize the accuracy rate of the weather feature matrix T, the divergence needs to be minimized. The gradient descent method is selected for iteration when finding the minimum divergence.

[0096] For sudden influencing factors, the output situation in a period of time before the prediction point is used as the input, and the one-dimensional convolutional neural network is used to extract the time series information to obtain the fluctuation status of the photovoltaic output in the past short time.

[0097] S1.1.2: Use the Adam algorithm to train the Bayesian neural network. This algorithm introduces a bias correction factor while considering the first-order and second-order matrix estimations to prevent the situation of excessive second-order matrix bias in the early stage of training. The specific steps of training the Bayesian neural network with the Adam algorithm are as follows:

[0098] (1) Calculate the decay averages of m t and v t :

[0099] First-order matrix estimation:

[0100] m t = β1 × m t-1 + (1 - β1) × dx (5)

[0101] Second-order matrix estimation:

[0102] v t = β2 × v t-1 + (1 - β2) × (dx) 2 (6)

[0103] In Equations (5) and (6): β1 is the exponential decay rate of the first-order matrix estimation; β2 is the exponential decay rate of the second-order matrix estimation, dx is the gradient; m t , v t are the first-order and second-order matrix estimation values respectively; m t-1 , v t-1 are the first-order and second-order matrix estimation values at the previous moment respectively.

[0104] (2) Perform bias correction to correct the first and second matrix estimations. First-moment estimation Second-moment estimation Bias correction:

[0105]

[0106]

[0107] In equations (7) and (8): m t ′, v t ′ are the correction values of the first-order and second-order matrix estimates respectively.

[0108] Update parameters:

[0109]

[0110] In equation (9), x t , x t+1 are parameter vectors; to avoid a denominator of 0, eps is a positive number close to 0; α represents the learning rate.

[0111] S1.1.3: Use the Monte Carlo sampling method and output the photovoltaic power output prediction value after multiple predictions.

[0112] S1.1.4: Obtain the relative error δ at each time point by comparing the photovoltaic power output prediction value obtained by the Monte Carlo sampling method with the actual photovoltaic power output value through equation (10) f :

[0113]

[0114] In equation (10): is the actual photovoltaic power output value at the f-th moment; y f is the photovoltaic power output prediction value at the f-th moment.

[0115] Step S1.2: Use the upper and lower limits where the relative error is located at any moment point as the state division value range, and obtain the state transition probability matrix of the relative error at the corresponding moment point for correcting the photovoltaic power output prediction value at the corresponding time point, so as to obtain the corrected photovoltaic power output prediction values at each time point;

[0116] S1.2.1: Use the mean - mean square deviation grading method to divide the predicted relative error into 4 states according to size: E1[-20%, -10%], E2[-10%, 0], E3[0, 10%], E4[10%, 20%], and establish a Markov state set. According to the Markov state set, the state transition probability matrix of the Bayesian neural network prediction result can be obtained. The solution process of the state transition probability matrix is as follows:

[0117] According to Markov chain theory, multiple states may occur in each experiment. If event E i occurs, then the event is in state E i state. State Ei From k steps to E j The probability P ij (k) :

[0118]

[0119] In formula (11): N ij (k) Is the number of transitions of the sample state from E i To E j ; N i Is the total number of times the state appears. Then the k-step state transition probability matrix P (k) Is:

[0120]

[0121] S1.2.2: The weighted Markov chain is an improvement on the Markov chain prediction. On the original basis, a weight is assigned to different prediction states, and then weighted summation is performed. Autocorrelation analysis is carried out on a certain amount of actual photovoltaic output values to obtain the autocorrelation coefficient. A larger weight is assigned to the prediction state with a larger absolute value of the autocorrelation coefficient. The autocorrelation coefficient r of each step length is obtained from formula (13) k :

[0122]

[0123] In formula (13): r k Is the k-th order autocorrelation coefficient; x i Is the sample data at time i; Is the average value of the sample data. The autocorrelation coefficient is normalized to obtain the weights w of each order k :

[0124]

[0125] Combining the weights of each order of data and the state transition probability matrix, the probability P of various states of the photovoltaic output prediction error data variable can be determined i :

[0126]

[0127] Taking the state corresponding to the maximum probability as the next turn of the variable, and then correcting the photovoltaic prediction relative error value according to this maximum probability and the upper and lower limits of the corresponding state interval to obtain the corrected value of the photovoltaic prediction value

[0128]

[0129] In formula (16): y f (1)is the correction value of the predicted photovoltaic output at the f-th moment; y f (0) is the predicted photovoltaic output at the f-th moment; d 1i is E i the upper limit value of the state; d 2i is E i the lower limit value of the state.

[0130] Step S1.3: According to the state transition probability matrix, use the weighted Markov chain to correct the improved Bayesian neural network prediction model to obtain the corrected improved Bayesian neural network, which is used to output the predicted photovoltaic output values at future moments;

[0131] Step S2: Obtain the system eigenvalues corresponding to the predicted photovoltaic output values at future moments based on the eigenvalue method:

[0132] As Figure 3 shown, obtaining the system eigenvalues corresponding to the predicted photovoltaic output values at future moments based on the eigenvalue method is carried out according to the following steps:

[0133] Step S2.1: Use the Lyapunov linearization method to process the equations describing the characteristics of the photovoltaic grid-connected power system to obtain the state equation matrix A of the photovoltaic grid-connected power system, and construct the mathematical relationships between the sensitivity of the system eigenvalue to the change in photovoltaic output and the sensitivity of the state equation matrix A to the change in photovoltaic output;

[0134] S2.1.1: The calculation of the eigenvalues is realized by the state equation coefficient matrix A. Therefore, first, it is necessary to calculate the photovoltaic grid-connected power The equations describing the characteristics of the photovoltaic grid-connected power system usually include algebraic equations and differential equations:

[0135] 0 = f(x, y) (17)

[0136]

[0137] In equations (17) and (18): x represents the state variables indicating the dynamic characteristics of the system in the differential equation system; y represents the operating parameters of the system in the algebraic equation system.

[0138] Algebraic equations such as: the SG machine-network interface equation:

[0139]

[0140] In equation (19): I xi 、I yi are the x-axis and y-axis components of the current at the i-th node respectively; U xi 、U yi are the x-axis and y-axis components of the voltage at the i-th node respectively; U xj, U yj are the x- and y-axis components of the voltage of the j-th node; G ii is the self-conductance of the i-th node; B ii is the self-susceptance of the i-th node; G ij is the mutual conductance between the i-th and j-th nodes; B ij is the mutual susceptance between the i-th and j-th nodes.

[0141]

[0142] In Equation (20): U di , U qi are the d- and q-axis components of the voltage of the i-th node; δ i is the power angle of the i-th node.

[0143]

[0144] In Equation (21): I di , I qi are the d- and q-axis components of the current of the i-th node; I Gxi , I Gyi are the x- and y-axis components of the current of the i-th node of the SG.

[0145] Grid-side current equation of the PV grid-connected inverter:

[0146]

[0147] In Equation (22): I gd , I gq are the d- and q-axis components of the grid-side current; U gd , U gq are the d- and q-axis components of the grid-side voltage; U d , U q are the d- and q-axis components of the PV node voltage; R T , X T are the resistance and reactance of the PV grid-connected line respectively.

[0148] Differential equations such as: Equation representing the mechanical transient of the SG:

[0149]

[0150] In Equation (23): δ G is the power angle of the SG; ω G is the rotational speed of the SG; ω B is the reference value of the rotational speed of the SG; T m is the mechanical torque of the SG; E′ q is the quadrature-axis transient electromotive force of the SG; X q is the quadrature-axis synchronous reactance of the SG; X′ dis the direct-axis transient reactance of SG; D G is the damping power coefficient; H G is the rotor inertia coefficient of SG; I d 、I q are the d-axis and q-axis components of the node current of SG respectively.

[0151] Control equation of the PV grid-connected inverter:

[0152]

[0153] In Equation (24): are the reference values of the d-axis and q-axis components of the grid-side current respectively; Q g 、 are the reactive power value and the reference value of the grid side respectively; k p1 、k i1 、k p2 、k i2 、k p3 、k i3 、k p4 、k i4 are the PI control parameters of the inverter.

[0154] Linearize Equations (17) and (18) at the steady-state operating point (x (0) , y (0) ), and obtain:

[0155]

[0156] In Equation (25):

[0157]

[0158]

[0159] Thus, the coefficient matrix of the system state equation can be obtained:

[0160]

[0161] S2.1.2: When the system is subjected to small disturbances, the coefficient matrix of the system state equation will also change accordingly, and the change of the matrix will lead to the uncertainty of the characteristic roots. At this time, the small disturbance is the randomness of the PV output. Therefore, the linear relationship between the system eigenvalues and the PV output fluctuation can be obtained by solving the sensitivity matrix. The sensitivity of the system state matrix is calculated by multiplying the left matrix w and the right matrix v. Let the PV output be P PV ;

[0162]

[0163] In Equation (27): is the sensitivity of the state matrix to the PV output; is the sensitivity of the photovoltaic output to the right - multiplying matrix; is the sensitivity of the eigenvalue to the photovoltaic output.

[0164]

[0165] In Equation (28): A T is the transpose of the state matrix.

[0166] The relational expression between the sensitivity of the eigenvalue to the photovoltaic output and the sensitivity of the state matrix to the photovoltaic output can be obtained:

[0167]

[0168] In Equation (29): w T is the transpose of the left - multiplying matrix.

[0169] Step S2.2: Regard the randomness of the photovoltaic output as a small perturbation in the photovoltaic grid - connected power system. By using the derivative method, obtain the sensitivity of the state - equation matrix A to the change in the photovoltaic output, and then obtain the sensitivity of the system eigenvalue to the change in the photovoltaic output according to the mathematical relational expression;

[0170] S2.2.1: It can be seen from the relational expression that in order to calculate the sensitivity of the system eigenvalue to the photovoltaic output it is necessary to first obtain the sensitivity of the state matrix to the photovoltaic output Since the parameter of the photovoltaic output does not explicitly appear in the state matrix, it is impossible to obtain pv by directly taking the partial derivative of the elements in A with respect to P Therefore, the derivative - definition method is selected for solution.

[0171]

[0172] In Equation (30): A(P pv ) and A(P pv +ΔP pv ) are the values of the system state matrix A before and after the change in the photovoltaic output respectively; ΔP pv is the change amount of the photovoltaic output.

[0173] When P pv is small enough for the entire state matrix A, Equation (31) can be written as:

[0174]

[0175] S2.2.2: After obtaining the value of can be calculated through Equation (29). For the small perturbation ΔP pv , the following approximate equivalence can be made:

[0176]

[0177] In Equation (32): Δλ τ is the change in eigenvalue.

[0178] It can be obtained that:

[0179]

[0180] Step S2.3: According to the predicted values of PV power output at future moments and the sensitivity of the change in PV power output to the system eigenvalues, obtain the system eigenvalues corresponding to the predicted values of PV power output at future moments;

[0181] S2.3.1: Let the sequence of predicted values of PV power output at future moments be denoted as P = {P pv1 , P pv2 , …, P pvφ , …, P pvn}, and the corresponding time sequence be t = {t1, t2, …, t φ , …, t n}, where t φ represents the φ-th moment, and P pvφ represents the predicted value of PV power output at the φ-th moment t φ ;

[0182] S2.3.2: Let the initial moment be t0, then the PV power output value at the initial moment t0 is denoted as P pv0 , and the τ-th system eigenvalue at the initial moment t0 is denoted as Use Equation (34) to calculate the τ-th system eigenvalue φ at the φ-th moment t

[0183]

[0184] In Equation (34): z is the number of system eigenvalues; P pvφ is the predicted value of PV power output at the φ-th moment t φ ; is the τ-th system eigenvalue at the initial moment t0;

[0185] S2.3.3: Use Equation (35) to obtain the system eigenvalue λ corresponding to the predicted values of PV power output at future moments:

[0186]

[0187] Step S3: Based on the sensitivity of the system eigenvalues to the operating parameters and control parameters of the PV grid-connected power system, and based on the system eigenvalues corresponding to the predicted values of PV power output at future moments, optimize the parameters affecting the stable operation of the PV system:

[0188] Step S3.1: Obtain the sensitivity of the system eigenvalues to the operating parameters and control parameters of the photovoltaic grid-connected power system, and obtain the dominant variables affecting the system eigenvalues.

[0189] Sa: Determine the photovoltaic system parameters to be optimized, including: operating parameters and control parameters; the operating parameter is the active power output P of the synchronous generator SG G ; the control parameter is the k of the grid-connected inverter p 、k i parameters, including k p1 、k i1 、k p2 、k i2 、k p3 、k i3 、k p4 、k i4 ;

[0190] Sb: Calculate the partial derivative of the variable affected by the operating parameter with respect to the operating parameter, and use it as an intermediate variable, so as to obtain the partial derivative of the state equation matrix A with respect to the operating parameter, which is the sensitivity of the system eigenvalue λ to the operating parameter.

[0191] The main difficulties in obtaining the sensitivity of the eigenvalue to the operating parameter are mainly the following two: there is a close relationship between the operating parameters, and when one parameter changes, many parameters in the state matrix will change; there are also some parameters that usually do not directly appear in the system state matrix, such as the active power output P of the SG G , which is usually reflected in voltage, electromotive force, power angle, and current. The SG dynamic model adopts a classical third-order model considering the excitation system and the speed regulation system, and the formula is as follows:

[0192]

[0193] In formula (36): E f is the excitation electromotive force; X d is the direct-axis reactance; X d ′ is the direct-axis open-circuit transient time constant; K A and T A are the excitation governor parameters; U ref is the voltage reference value; T g is the governor inertia time constant; T m0 is the initial value of T m ; k m is the governor droop coefficient.

[0194] The power equation corresponding to the DC capacitor on the photovoltaic side is:

[0195]

[0196] In Equation (37): U dc is the DC capacitor voltage; C dc is the DC capacitance value.

[0197] When obtaining the eigenvalue pair P G sensitivity, it cannot be directly obtained by taking the derivative of A. Therefore, an indirect method is used to solve it: First, find the partial derivative of the elements affected by P G with respect to P G , and use it as an intermediate variable to indirectly obtain the partial derivative of A with respect to P G .

[0198] Sb.1: Divide the state matrix A into four submatrices, denoted as A1, B1, C1, and D1 respectively:

[0199] Sb.2: Use Equation (38) to obtain the variables in submatrix A1 affected by the active power output P G of the synchronous generator SG, including: variables composed of the operating parameters of the synchronous generator SG and variables composed of the operating parameters of the photovoltaic system

[0200]

[0201] In Equation (38): X d is the direct-axis reactance of the synchronous generator SG; T d ′0 is the direct-axis open-circuit transient time constant of the synchronous generator SG; X d ′ is the direct-axis transient reactance of the synchronous generator SG; N G and N P are the number of nodes of the synchronous generator SG and the number of photovoltaic nodes respectively; N G ×N G represents the dimension of submatrix A1 corresponding to the number of nodes of the synchronous generator SG, and N P ×N P represents the dimension of submatrix A1 corresponding to the number of photovoltaic nodes; I d is the d-axis component of the current of the synchronous generator SG; U dc is the DC capacitor voltage; C dc is the DC capacitance value; I gd , I gq are the d- and q-axis components of the grid-side current respectively; U gd , U gq are the d- and q-axis components of the grid-side voltage respectively;

[0202] Sb3: Use Equation (39) to obtain the sensitivity of submatrix A1 to the active power output P G :

[0203]

[0204] In Equation (39): P Gm is the active power output of the m-th SG; (:,m) represents the m-th column of the matrix, and there is:

[0205]

[0206] Sb4: Obtain the variables in sub-matrix B1 affected by the active power output P of the synchronous generator SG G including: the first variable composed of the operating parameters of the synchronous generator SG and the second variable

[0207]

[0208] Sb5: Obtain the sensitivity of sub-matrix B1 to the active power output P G using Equation (42):

[0209]

[0210] and there is:

[0211]

[0212] Sb6: Obtain the variables in sub-matrix C1 affected by the active power output P of the synchronous generator SG G including: the first variable composed of the operating parameters of the photovoltaic system and the second variable

[0213]

[0214] Sb7: Obtain the sensitivity of sub-matrix C1 to the active power output P G using Equation (45):

[0215]

[0216] Sb8: Obtain the variables in sub-matrix D1 affected by the active power output P of the synchronous generator SG G including: the variables composed of the operating parameters of the synchronous generator SG

[0217]

[0218] Sb9: Obtain the sensitivity of sub-matrix D1 to the active power output P G using Equation (47):

[0219]

[0220] Sc: Obtain the sensitivity of the system eigenvalue λ to the active power output P using Equation (48). G :

[0221]

[0222] In Equation (13): v is the right - multiplying matrix; w is the left - multiplying matrix; w T is the transpose of the left - multiplying matrix.

[0223] Sd: Calculate the sensitivity of the system eigenvalue λ to the control parameter:

[0224] Sd1: Calculate the partial derivatives of the state matrix A with respect to the k P1 parameter and k i1 parameter:

[0225]

[0226] In Equation (49): ω B is the rotational speed reference value of the step - generator SG.

[0227] Sd2: Calculate the partial derivatives of the state matrix A with respect to the k P2 parameter and k i2 parameter:

[0228]

[0229] Sd3: Calculate the partial derivatives of the state matrix A with respect to the k P3 parameter and k i3 parameter:

[0230]

[0231] Sd4: Calculate the partial derivatives of the state matrix A with respect to the k P4 parameter and k i4 parameter:

[0232]

[0233] Se: Obtain the sensitivity of the system eigenvalue λ to the k Pa parameter and k ia parameter (a = 1, 2, 3, 4) using Equation (18):

[0234]

[0235] Sf: Select the variable corresponding to the maximum sensitivity as the dominant variable affecting the system eigenvalue.

[0236] Step S3.2: Optimize the dominant variables of the system eigenvalues in the dangerous area. When all system eigenvalues are in the safe area, the optimization process ends to improve the stability of the PV - grid - connected power system.

[0237] Express the system eigenvalue λ τ in complex form:

[0238] λ τ = σ τ + jω τ (54)

[0239] Then the damping ratio ζ τ is:

[0240]

[0241] According to Figure 4 it can be known that when σ τ < 0 and ζ τ ≥ 0.05, this eigenvalue is in the safe region, while when σ τ ≥ 0, or σ τ < 0 and ζ τ < 0.05, it is in the dangerous region.

[0242] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above small disturbance stability optimization method, and the processor is configured to execute the program stored in the memory.

[0243] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is run by a processor, it executes the steps of the above small disturbance stability optimization method.

Claims

1. A small-signal stability optimization method for a power system based on random photovoltaic power output, which is applied to a power system with photovoltaic access, is characterized in that: The small disturbance stability analysis method is carried out according to the following steps: Step S1: Quantification of the uncertainty of photovoltaic power output: Step S1.1: Obtain weather characteristics, historical operation data of the photovoltaic power station, and time factors and input them into the improved Bayesian neural network for prediction to obtain the predicted values of the photovoltaic power output at each time point, and compare them with the corresponding actual values to obtain the relative error at each time point; Step S1.2: Take the upper and lower limits where the relative error at any moment point is located as the state division value range, and obtain the state transition probability matrix of the relative error at the corresponding moment point for correcting the predicted value of the photovoltaic power output at the corresponding time point, so as to obtain the corrected predicted values of the photovoltaic power output at each time point; Step S1.3: According to the state transition probability matrix, use the weighted Markov chain to correct the improved Bayesian neural network prediction model to obtain the corrected improved Bayesian neural network for outputting the predicted values of the photovoltaic power output at future moments; Step S2: Obtain the system eigenvalues corresponding to the predicted values of the photovoltaic power output at future moments based on the eigenvalue method: Step S2.1: Use the Lyapunov linearization method to process the equations describing the characteristics of the photovoltaic grid-connected power system to obtain the state equation matrix A of the photovoltaic grid-connected power system, and construct the mathematical relationships between the sensitivity of the system eigenvalues to the change of the photovoltaic power output and the sensitivity of the state equation matrix A to the change of the photovoltaic power output; Step S2.2: Regard the randomness of the photovoltaic power output as a small disturbance in the photovoltaic grid-connected power system, obtain the sensitivity of the state equation matrix A to the change of the photovoltaic power output through the derivative method, and then obtain the sensitivity of the system eigenvalues to the change of the photovoltaic power output from the mathematical relationship; Step S2.3: According to the predicted values of the photovoltaic power output at future moments and the sensitivity of the system eigenvalues to the change of the photovoltaic power output, obtain the system eigenvalues corresponding to the predicted values of the photovoltaic power output at future moments; Step S3: Optimize the parameters affecting the stable operation of the photovoltaic system based on the sensitivity of the system eigenvalues to the operation parameters and control parameters of the photovoltaic grid-connected power system and the system eigenvalues corresponding to the predicted values of the photovoltaic power output at future moments: Step S3.1: Obtain the sensitivity of the system eigenvalues to the operation parameters and control parameters of the photovoltaic grid-connected power system to obtain the dominant variables affecting the system eigenvalues; Step S3.2: Optimize the dominant variables of the system eigenvalues in the dangerous area. When all system eigenvalues are in the safe area, the optimization process ends to improve the stability of the photovoltaic grid-connected power system.

2. The small disturbance stability optimization method for a power system based on photovoltaic random power output according to claim 1, wherein The said Step S2.3 includes: S2.3.1: Let the predicted photovoltaic output value sequence at each future moment be denoted as P = {P pv1 , P pv2 , …, P pvj , …, P pvn}, and the corresponding time sequence of P be t = {t1, t2, …, t j , …, t n}, where t j represents the j-th moment, and P pvj represents the predicted photovoltaic output value at the j-th moment t j ; S2.3.2: Let the initial time be t0, then the PV output value at the initial time t0 is denoted as P pv0 , and the i-th system eigenvalue at the initial time t0 is denoted as Calculate the i-th system eigenvalue at the j-th time t using Equation (1) j ​ In Equation (1): k is the number of system eigenvalue; P PVj is the predicted value of photovoltaic output at the j-th moment t j ; is the i-th system eigenvalue at the initial moment t0; S2.3.3: Use Equation (2) to obtain the system eigenvalue λ corresponding to the predicted values of the photovoltaic power output at future moments; 3. The small disturbance stability optimization method for a power system based on photovoltaic random power output according to claim 2, characterized in that The said Step S3.1 includes: Sa: Determine the parameters of the photovoltaic system to be optimized, including: operating parameters and control parameters; the operating parameter is the active power output P of the synchronous generator SG G ; the control parameter is the k p parameter, k i parameter, including k p1 parameter, k i1 parameter, k p2 parameter, k i2 parameter, k p3 parameter, k i3 parameter, k p4 parameter, k i4 parameter; Sb: Calculate the partial derivative of the variable affected by the operation parameter with respect to the operation parameter and use it as an intermediate variable, so as to obtain the partial derivative of the state equation matrix A with respect to the operation parameter, which is the sensitivity of the system eigenvalue λ to the operation parameter; Sb.1: Divide the state matrix A into four sub-matrices, denoted as A1, B1, C1, and D1 respectively: Sb.2: Obtain the variables in the sub-matrix A1 affected by the active power output P of the synchronous generator SG using Equation (3), including: variables composed of the operating parameters of the synchronous generator SG G and variables composed of the operating parameters of the photovoltaic system as well as variables composed of the operating parameters of the photovoltaic system In Equation (3): X d is the direct-axis reactance of the synchronous generator SG; T d ′0 is the direct-axis open-circuit transient time constant of the synchronous generator SG; X d ′ is the direct-axis transient reactance of the synchronous generator SG; N G and N P are the number of nodes of the synchronous generator SG and the number of photovoltaic nodes, respectively; N G ×N G represents the dimension of the sub-matrix A1 corresponding to the number of nodes of the synchronous generator SG, and N P ×N P represents the dimension of the sub-matrix A1 corresponding to the number of photovoltaic nodes; I d is the d-axis component of the current of the synchronous generator SG; U dc is the DC capacitor voltage; C dc is the DC capacitance value; I gd and I gq are the d- and q-axis components of the grid-side current, respectively; U gd and U gq are the d- and q-axis components of the grid-side voltage, respectively; Sb3: Obtain the sensitivity of the sub-matrix A1 to the active power output P using Equation (4) G : In Equation (4): P Gm is the active power output of the m-th SG; (:, m) represents the m-th column of the matrix, and there is: Sb4: Obtain the variables affected by the active power output P of the synchronous generator SG in the sub-matrix B1 using Equation (6), including: the first variable composed of the operating parameters of the synchronous generator SG G and the second variable ​ Sb5: Obtain the sensitivity of the submatrix B1 to the active power output P using Equation (7) G : And there is: Sb6: Obtain the variables in sub-matrix C1 affected by the active power output P of synchronous generator SG using Equation (9), including: the first variable composed of photovoltaic operation parameters G and the second variable ​ Sb7: Obtain the sensitivity of the submatrix C1 to the active power output P using Equation (10) G : Sb8: Obtain the variables in sub-matrix D1 affected by the active power output P of synchronous generator SG using Equation (11), including: the variables composed of the operating parameters of synchronous generator SG G The variables affected by the active power output P of synchronous generator SG include: the variables composed of the operating parameters of synchronous generator SG Sb9: Obtain the sensitivity of the sub-matrix D1 to the active power output P using Equation (12) G : Sc: Obtain the sensitivity of the system eigenvalue λ to the active power output P using Equation (13): G ​ In formula (13): v is the right multiplication matrix; w is the left multiplication matrix; w T is the transpose of the left multiplication matrix; Sd: Obtain the sensitivity of the system eigenvalue λ to the control parameter: Sd1: Obtain the partial derivative of the state matrix A with respect to the k P1 parameter, k i1 parameter: In Equation (14): ω B is the reference value of the rotational speed of the synchronous generator SG; Sd2: Obtain the partial derivative of the state matrix A with respect to the k P2 parameter, k i2 parameter: Sd3: Obtain the partial derivative of the state matrix A with respect to the k P3 parameter, k i3 parameter: Sd4: Obtain the partial derivative of the state matrix A with respect to the k P4 parameter, k i4 parameter: Se: Obtain the sensitivity of the system eigenvalue λ with respect to the parameter k using Equation (18) Pa parameter, k ia sensitivity of the parameter, a = 1, 2, 3, 4: Sf: Select the variable corresponding to the maximum sensitivity as the dominant variable affecting the system eigenvalues.

4. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program for supporting the processor to execute the small disturbance stability optimization method described in claim 1 or 2 or 3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the small disturbance stability optimization method described in claim 1 or 2 or 3.

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